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The Markov chain Monte Carlo (MCMC) method is widely used in various fields as a powerful numerical integration technique for systems with many degrees of freedom. In MCMC methods, probabilistic state transitions can be considered as a random walk in state space, and random walks allow for sampling from complex distributions. However, paradoxically, it is necessary to carefully suppress the randomness of the random walk to improve computational efficiency. By breaking detailed balance, we can create a probability flow in the state space and perform more efficient sampling along this flow. Motivated by this idea, practical and efficient nonreversible MCMC methods have been developed over the past ten years. In particular, the lifting technique, which introduces probability flows in an extended state space, has been applied to various systems and has proven more efficient than conventional reversible updates. We review and discuss several practical approaches to implementing nonreversible MCMC methods, including the shift method in the cumulative distribution and the directed-worm algorithm. [ABSTRACT FROM AUTHOR]

An approach is presented for simulating multipulse nuclear magnetic resonance (NMR) spectra of polycrystalline solids directly in the frequency domain. The approach integrates the symmetry pathway concept for multipulse NMR with efficient algorithms for calculating spinning sideband amplitudes and performing interpolated finite-element numerical integration over all crystallite orientations in a polycrystalline sample. The numerical efficiency is achieved through a set of assumptions used to approximate the evolution of a sparse density matrix through a pulse sequence as a set of individual transition pathway signals. The utility of this approach for simulating the spectra of complex materials, such as glasses and other structurally disordered materials, is demonstrated. [ABSTRACT FROM AUTHOR]

In this work, rate coefficients of four prototypical insertion reactions, X + H2 → H + XH (X = C(1D), N(2D), O(1D), S(1D)), and associated isotope reactions are calculated based on ring polymer molecular dynamics (RPMD) with Cayley propagator (Cayley-RPMD). The associated kinetic isotope effects are systematically studied too. The Cayley propagator used in this work increases the stability of numerical integration in RPMD calculations and also supports a larger evolution time interval, allowing us to reach both high accuracy and efficiency. So, our results do not only provide chemical kinetic data for the title reactions in an extended temperature range but also consist of experimental results, standard RPMD, and other theoretical methods. The results in this work also reflect that Cayley-RPMD has strong consistency and high reliability in its investigations of chemical dynamics for insertion reactions. [ABSTRACT FROM AUTHOR]

Open-source APOST-3D software features a large number of wavefunction analysis tools developed over the past 20 years, aiming at connecting classical chemical concepts with the electronic structure of molecules. APOST-3D relies on the identification of the atom in the molecule (AIM), and several analysis tools are implemented in the most general way so that they can be used in combination with any chosen AIM. Several Hilbert-space and real-space (fuzzy atom) AIM definitions are implemented. In general, global quantities are decomposed into one- and two-center terms, which can also be further grouped into fragment contributions. Real-space AIM methods involve numerical integrations, which are particularly costly for energy decomposition schemes. The current version of APOST-3D features several strategies to minimize numerical error and improve task parallelization. In addition to conventional population analysis of the density and other scalar fields, APOST-3D implements different schemes for oxidation state assignment (effective oxidation state and oxidation states localized orbitals), molecular energy decomposition schemes, and local spin analysis. The APOST-3D platform offers a user-friendly interface and a comprehensive suite of state-of-the-art tools to bridge the gap between theory and experiment, representing a valuable resource for both seasoned computational chemists and researchers with a focus on experimental work. We provide an overview of the code structure and its capabilities, together with illustrative examples. [ABSTRACT FROM AUTHOR]

A new algorithm has been developed to simulate two-dimensional (2D) spectra with correlated anisotropic frequencies faster and more accurately than previous methods. The technique uses finite-element numerical integration on the sphere and an interpolation scheme based on the Alderman–Solum–Grant algorithm. This method is particularly useful for numerical calculations of joint probability distribution functions involving quantities with a parametric orientation dependence. The technique's efficiency also allows for practical least-squares fitting of experimental 2D solid-state nuclear magnetic resonance (NMR) datasets. The simulation method is illustrated for select 2D NMR methods, and a least-squares analysis is demonstrated in the extraction of paramagnetic shift and quadrupolar coupling tensors and their relative orientation from the experimental shifting-d echo 2H NMR spectrum of a NiCl2 · 2D2O salt. [ABSTRACT FROM AUTHOR]

block2 is an open source framework to implement and perform density matrix renormalization group and matrix product state algorithms. Out-of-the-box it supports the eigenstate, time-dependent, response, and finite-temperature algorithms. In addition, it carries special optimizations for ab initio electronic structure Hamiltonians and implements many quantum chemistry extensions to the density matrix renormalization group, such as dynamical correlation theories. The code is designed with an emphasis on flexibility, extensibility, and efficiency and to support integration with external numerical packages. Here, we explain the design principles and currently supported features and present numerical examples in a range of applications. [ABSTRACT FROM AUTHOR]

Typically, the parameters entering a physical simulation model carry some kind of uncertainty, e.g., due to the intrinsic approximations in a higher fidelity theory from which they have been obtained. Global sensitivity analysis (GSA) targets quantifying which parameter uncertainties impact the accuracy of the simulation results, e.g., to identify which parameters need to be determined more accurately. We present a GSA approach based on the Cramérs–von Mises distance. Unlike prevalent approaches, it combines the following properties: (i) it is equally suited for deterministic as well as stochastic model outputs, (ii) it does not require gradients, and (iii) it can be estimated from numerical quadrature without further numerical approximations. Using quasi-Monte Carlo for numerical integration and a first-principles kinetic Monte Carlo model for the CO oxidation on RuO2(110), we examine the performance of the approach. We find that the results agree very well with what is known in the literature about the sensitivity of this model and that the approach converges in a modest number of quadrature points. Furthermore, it appears to be robust against even extreme relative noise. All these properties make the method particularly suited for expensive (kinetic) Monte Carlo models because we can reduce the number of simulations as well as the target variance of each of these. [ABSTRACT FROM AUTHOR]

For a detailed understanding of many processes in nature involving, for example, energy or electron transfer, the theory of open quantum systems is of key importance. For larger systems, an accurate description of the underlying quantum dynamics is still a formidable task, and, hence, approaches employing machine learning techniques have been developed to reduce the computational effort of accurate dissipative quantum dynamics. A downside of many previous machine learning methods is that they require expensive numerical training datasets for systems of the same size as the ones they will be employed on, making them unfeasible to use for larger systems where those calculations are still too expensive. In this work, we will introduce a new method that is implemented as a machine-learned correction term to the so-called Numerical Integration of Schrödinger Equation (NISE) approach. It is shown that this term can be trained on data from small systems where accurate quantum methods are still numerically feasible. Subsequently, the NISE scheme, together with the new machine-learned correction, can be used to determine the dissipative quantum dynamics for larger systems. Furthermore, we show that the newly proposed machine-learned correction outperforms a previously handcrafted one, which, however, improves the results already considerably. [ABSTRACT FROM AUTHOR]

In this paper, we consider the constrained estimation problem for the binomial AR(1) model using Bayesian approach. We show that by using Gibbs sampling algorithm, the constrains for the parameters and latent variables can be routinely implemented. While obtaining all the full conditional distributions under the unconstrained environment, we only need to generate samples from them and make restrictions to easily described cross-sections, respectively, which avoids complex numerical integrations under the overall constraint set. In the simulation study, the performance of our algorithm is checked. Finally, the method is applied to two real data examples. [ABSTRACT FROM AUTHOR]

ABSTRACT Currently, our understanding of material‐scale deterioration resulting from meteorologically induced variations in pore water pressure and its significant impact on infrastructure slopes is limited. To bridge this knowledge gap, we have developed an extended kinematic hardening constitutive model for unsaturated soils that refines our understanding of weather‐driven deterioration mechanisms in heterogeneous clay soils. This model has the capability of predicting the irrecoverable degradation of strength and stiffness that has been shown to occur when soils undergo wetting and drying cycles. The model is equipped with a fully coupled and hysteretic water retention curve and a hysteretic loading–collapse curve and has the capability to predict the irrecoverable degradation of strength and stiffness that occurs during cyclic loading of soils. Here, we employ a fully implicit stress integration technique and give particular emphasis to deriving a consistent tangent operator, which includes the linearisation of the retention curve. The proposed algorithm is evaluated for efficiency and performance by simulating various stress and strain‐driven triaxial paths, and the accuracy of the integration technique is evaluated through the use of convergence curves. [ABSTRACT FROM AUTHOR]

The article "Commentary: Accelerating spiking neural network simulations with PymoNNto and PymoNNtorch" published in Frontiers in Neuroinformatics compares different simulators for spiking neural networks. The study reveals that discrepancies in firing rates between simulators are due to the use of an unsuitable numerical integration method. The analysis confirms that only NEST simulator accurately simulates the model mathematically. The study also uncovers a subtle bug in NESTML and emphasizes the importance of precise benchmarks in simulation studies. [Extracted from the article]

Numerical tesseroid and radial-type approaches are presented and compared in terms of their efficiency for deriving the regional geoid height, vertical gravity, and gradiometric anomalies from sea floor topography grids. The vertical gradient function is particularly suitable for representing shorter wavelengths of gravity, typically less than 10 km. These two modeling methods were applied to the Great Meteor guyot in the Atlantic Ocean using its bathymetry. To optimize the computation of high-resolution gravity anomalies, the Armadillo, GSL, and OpenMP libraries were used to provide an environment for fast vector implementation, numerical integration for tesseroid calculation, and parallelization for loop iterations, resulting in a computation speed increase. The tesseroid and radial methods remain equivalent up to a resolution of about 1 min, with the radial method being faster when dealing with a large number of model points for the geoid. Aside from optimization enabling high-resolution gravity simulations, these fast modeling data can be used as the main operators in gravimetric inversion or to reduce the terrain effects in gravity observations, revealing gravity and sedimentary layers. [ABSTRACT FROM AUTHOR]

In previous studies, radar reflectivity is often directly assimilated using reflectivity operators based on a single-moment (SM) microphysics scheme, though the forecast model uses a double-moment (DM) microphysics scheme. With the fixed number concentrations, only the mixing ratios of hydrometeors are directly updated during the assimilation, which leads to a mismatch between the analyzed microphysical state variables and the microphysics scheme of the forecast model. In this study, the radar reflectivity is directly assimilated through an observation operator consistent with the DM Thompson microphysics scheme used in numerical integrations, and the impact of reflectivity operators based on SM and DM schemes on the analysis performance of the ensemble Kalman filter for typhoon Lekima on 9 August 2019 is evaluated. Reflectivity observations from a single operational weather radar in Wenzhou City, Zhejiang Province of China are assimilated. In addition, the dual-polarization observations from the same radar are used to evaluate the quality of the analysis. The analyzed reflectivity and dual-polarization characteristics obtained by different reflectivity operators are examined in detail. Compared with the experiments applying the reflectivity operator based on the SM Lin scheme, the use of a reflectivity operator consistent with the DM Thompson scheme adopted in the forecast model results in analyzed reflectivity and polarization characteristics that are more consistent with the observed characteristics in terms of general structure, location, and intensity. Forecasted reflectivity, 3 h accumulated precipitation, and typhoon intensity and track are also evaluated. The application of the reflectivity operator based on the DM scheme makes better forecasts of typhoon intensity, precipitation, and reflectivity, which also improves the forecast skills on typhoon tracks to a certain extent. [ABSTRACT FROM AUTHOR]

Combining the Liouville equations for polar motion (PM) with forecasted geophysical effective angular momentum (EAM) functions can significantly improve the accuracy of Earth's PM predictions. These predictions rely on deconvolution and convolution methods. Deconvolution derives the geodetic EAM function from the PM observations, while convolution uses both the geodetic and geophysical EAM functions to reproduce and predict the PM values. However, there are limitations in existing numerical realisations of deconvolution and convolution that must be addressed. These limitations include low-frequency biases, high-frequency errors, and edge errors, which can negatively impact the accuracy of PM prediction. To overcome these concerns, we develop the Convolution Least Squares (Conv-LS) scheme through a multi-perspective analysis in the frequency domain, PM domain, and EAM domain. By comparing representative approaches for reproducing three different PM series (IERS C01, IERS C04, and IGS) with varying sampling intervals (18.25 days, daily, and 6 h), we demonstrate that the Conv-LS scheme can effectively eliminate the usually present spurious signals and also integrate high-accuracy deconvolution algorithms to reduce reproduced errors further. Compared to the traditional approacsh (using a low-accuracy discrete PM equation for deconvolution and numerical integration for convolution), our new approach (utilising a high-accuracy deconvolution algorithm along with the Conv-LS scheme for convolution) reduces the standard deviations of the residuals' x-component by 31.0%, 60.1%, and 13.7% for C01, C04, and IGS PM series, respectively, while also reducing the y-component by 17.3%, 47.0%, and 14.0%, respectively. These results highlight the superiority of the Conv-LS scheme, leading us to recommend it for practical applications. [ABSTRACT FROM AUTHOR]

This paper deals with the local bifurcation analysis of a nanotube with a nanostring passing through it. Eringen's two-phase local/nonlocal model and Eringen's differential model are employed as constitutive equations. The governing equations are derived as two nonlinear first-order systems of ordinary differential equations. Nonlinear analysis is performed by using the Lyapunov–Schmidt method. The influence of the small length scale parameter and the phase parameter on critical buckling load, type of bifurcation and post-buckling shape of the nanotube is examined for both types of constitutive equations. Depending on the values of the small length scale parameter and the phase parameter, the critical buckling load corresponding to Eringen's two-phase local/nonlocal model can be greater or less than that corresponding to Eringen's differential model. It is shown that for both models supercritical pitchfork bifurcation occurs. The post-buckling shapes of nanotube, obtained by numerical integration, exhibit a qualitative difference between the two models. [ABSTRACT FROM AUTHOR]

As commonly known, standard time integration of the kinematic equations of rigid bodies modeled with three rotation parameters is infeasible due to singular points. Common workarounds are reparameterization strategies or Euler parameters. Both approaches typically vary in accuracy depending on the choice of rotation parameters. To efficiently compute different kinds of multibody systems, one aims at simulation results and performance that are independent of the type of rotation parameters. As a clear advantage, Lie group integration methods are rotation parameter independent. However, few studies have addressed whether Lie group integration methods are more accurate and efficient compared to conventional formulations based on Euler parameters or Euler angles. In this paper, we close this gap using the R 3 × S O (3) Lie group formulation and several typical rigid multibody systems. It is shown that explicit Lie group integration methods outperform the conventional formulations in terms of accuracy. However, it turns out that the conventional Euler parameter-based formulation is the most accurate one in the case of implicit integration, while the Lie group integration method is computationally the more efficient one. It also turns out that Lie group integration methods can be implemented at almost no extra cost in an existing multibody simulation code if the Lie group method used to describe the configuration of a body is chosen accordingly. [ABSTRACT FROM AUTHOR]

This paper proposes a heterogeneous time integration algorithm to analyze the dynamic response of structures with localized hysteretic nonlinearities. The critical point is to treat the whole structure as a combination of a linear substructure governed by the second-order dynamic equation and a nonlinear substructure controlled by the first-order differential formulation. With this partitioning, tailored numerical integration algorithms with heterogeneous time steps are applied directly to calculate the displacements and hysteretic forces from the linear and the nonlinear substructures, respectively. Subsequently, the dynamic responses of the whole structure are solved by a predictor–corrector procedure, where the hysteretic forces and displacement responses are coupled and exchanged to update the partitioning solutions. Furthermore, the energy balance method is derived to verify the stability of the proposed heterogeneous time integration algorithm. Dynamic responses of structures with friction damper, hysteretic models, and bolted joint models are studied to demonstrate the accuracy and efficiency of the proposed algorithm. [ABSTRACT FROM AUTHOR]

The virtual element method (VEM) is a stabilized Galerkin method on meshes that consist of arbitrary (convex and nonconvex) polygonal and polyhedral elements. A crucial ingredient in the implementation of low‐ and high‐order VEM is the numerical integration of monomials and nonpolynomial functions over such elements. In this article, we apply the recently proposed scaled boundary cubature (SBC) scheme to compute the weak form integrals in various virtual element formulations over polygonal and polyhedral meshes. In doing so, we demonstrate the flexibility of the approach and the accuracy that it delivers on a broad suite of boundary‐value problems in 2D and 3D over polytopes with affine faces as well as on elements with curved boundaries. In addition, the use of the SBC scheme is exemplified in an enriched Poisson formulation of the VEM in which weakly singular functions are required to be integrated. This study establishes the SBC method as a simple, accurate and efficient integration scheme for use in the VEM. [ABSTRACT FROM AUTHOR]

Estimating parameters of dynamic models from experimental data is a challenging, and often computationally-demanding task. It requires a large number of model simulations and objective function gradient computations, if gradient-based optimization is used. In many cases, steady-state computation is a part of model simulation, either due to steady-state data or an assumption that the system is at steady state at the initial time point. Various methods are available for steady-state and gradient computation. Yet, the most efficient pair of methods (one for steady states, one for gradients) for a particular model is often not clear. In order to facilitate the selection of methods, we explore six method pairs for computing the steady state and sensitivities at steady state using six real-world problems. The method pairs involve numerical integration or Newton's method to compute the steady-state, and—for both forward and adjoint sensitivity analysis—numerical integration or a tailored method to compute the sensitivities at steady-state. Our evaluation shows that all method pairs provide accurate steady-state and gradient values, and that the two method pairs that combine numerical integration for the steady-state with a tailored method for the sensitivities at steady-state were the most robust, and amongst the most computationally-efficient. We also observed that while Newton's method for steady-state computation yields a substantial speedup compared to numerical integration, it may lead to a large number of simulation failures. Overall, our study provides a concise overview across current methods for computing sensitivities at steady state. While our study shows that there is no universally-best method pair, it also provides guidance to modelers in choosing the right methods for a problem at hand. [ABSTRACT FROM AUTHOR]

Bipolar plates (BPPs) and membrane electrode assemblies (MEAs) are the key components for proton exchange membrane fuel cells (PEMFCs), they are alternately arranged to construct a compact stack with high power generation. This stacking method may introduce several issues, such as the difficulties in maintenance, imprecise assembly and sealing. This paper presents a novel integrated packaged single fuel cell that employs titanium metal bipolar plates to construct a short stack with superior sealing performance and working reliability. To predict the performance of integrated packaged single cell, numerical model was developed to analyze the mass transfer of O 2 , H 2 and H 2 O within the cell, revealing a uniform distribution of reactants and current. A short stack was manufactured with 10 layers of single cells, it retains excellent sealing properties and consistent output across a range of pressure conditions, with a leakage rate deviation lower than 0.03 mL/(min·cell) and membrane current density variation less than 5%. Finally, the electrochemical performance of the integrated packaged short stack was tested, its maximum power is 886.67 mW/cm2. It can achieve a rated output power of 169.14 W and an energy density of 1684.97 mW/cm3. Thus, our developed short stack has high energy utilization efficiency for power generation, and is anticipated to provide a durable power source for drones, robots and new energy vehicles. • An integrated packaged single fuel cell short stack based on titanium metal polar plates was proposed. • Numerical model of single cell was established, simulation on gas molar concentration and current density distribution was conducted. • A 10-layer integrated short stack was fabricated, assembly stress and polarization tests verified its good sealing performance. [ABSTRACT FROM AUTHOR]

The aim of the present paper is first to propose a state-of-art of this domain. Second, some convergence results are established in the case of the Dirichlet distribution. This distribution has the advantage to include both the uniform case and the deterministic one. In a first part, the Dirichlet distribution is defined and some properties are supplied. In a second part, new results are established in connexion with former theorems. [ABSTRACT FROM AUTHOR]

Normal ogive (NO) models have contributed substantially to the advancement of item response theory (IRT) and have become popular educational and psychological measurement models. However, estimating NO models remains computationally challenging. The purpose of this paper is to propose an efficient and reliable computational method for fitting NO models. Specifically, we introduce a novel and unified expectation‐maximization (EM) algorithm for estimating NO models, including two‐parameter, three‐parameter, and four‐parameter NO models. A key improvement in our EM algorithm lies in augmenting the NO model to be a complete data model within the exponential family, thereby substantially streamlining the implementation of the EM iteration and avoiding the numerical optimization computation in the M‐step. Additionally, we propose a two‐step expectation procedure for implementing the E‐step, which reduces the dimensionality of the integration and effectively enables numerical integration. Moreover, we develop a computing procedure for estimating the standard errors (SEs) of the estimated parameters. Simulation results demonstrate the superior performance of our algorithm in terms of its recovery accuracy, robustness, and computational efficiency. To further validate our methods, we apply them to real data from the Programme for International Student Assessment (PISA). The results affirm the reliability of the parameter estimates obtained using our method. [ABSTRACT FROM AUTHOR]

Real-time hybrid test is an economical and efficient testing method to evaluate nonlinear structural performance. During the operation of real-time hybrid test, the time delay caused by the operating error of the actuator results in the worse stability and accuracy of the real-time hybrid test. To compensate for the delay of the actuator, the stability of the hybrid test system and the accuracy of the test are improved. In this paper, the advantages of the numerical integration algorithm and the linear acceleration extrapolation method are composed organically, and then a universal linear extrapolation-Newmark optimization compensation strategy is proposed to compensate for the time delay. Under the action of different seismic waves with and without the optimized compensation strategy, the self-developed DELTA-OpenSees real-time hybrid test system is used to comprehensively compare and analyze the real-time hybrid test of three-story frame structure with linear springs. The root mean square error and maximum error amplitude of the maximum error amplitude of the optimization results can reach 2.73% and 2.18%, respectively, which proves that the developed linear extrapolation-Newmark optimization compensation strategy can effectively improve the stability and accuracy of the real-time hybrid test system, and the optimization compensation strategy has good tracking performance and robustness. [ABSTRACT FROM AUTHOR]

We have carried out a detailed study of the Gamma-Ray Burst (GRB) photospheric emission model predicting a quasi-blackbody spectrum slightly broader than a Planck function. This model was suggested within the relativistic fireball dynamics for interpreting a still not well understood thermal component in the GRB prompt emission, recently observed by the GBM (Gamma-ray Burst Monitor) on board the Fermi space telescope. We propose a Monte Carlo (M C) code for elucidating the observed spectrum, the outflow dynamics and its geometry for a basic and a structured plasma jets whose parameters are implemented. The code involves a simulation part describing the photon propagation assuming an unpolarized, non-dissipative relativistic outflow and a data analysis part for exploring main photospheric emission properties such as the energy, arrival time and observed flux of the simulated seed photons and the photospheric radius. Computing the latter two observables by numerical integration, we obtained values very concordant with the M C simulated results. Fitting Band functions to the photon spectra generated by this method, we derived best-fit values of the photon indices matching well those featuring the observed spectra for most typical GRBs, but corresponding to fit functions inconciliable with blackbody spectral shapes. Various derived results are reported, compared to previous ones and discussed. They show to be very sensitive to the structure of the Lorentz factor that plays a crucial role in determining the presence and strength of geometrical effects. The latter manifest themselves by large broadenings of the simulated spectra featured by multiple peak energies consistently with GRB observations. They are assumed, with multiple Compton scattering, to produce bumps pointed out at very low photon energies. The interpretation of GRB observations is further performed via a Band spectral analysis using the RMFIT software. Finally, developments of this work are put into perspective. [ABSTRACT FROM AUTHOR]

We focus on learning unknown dynamics from data using ODE-nets templated on implicit numerical initial value problem solvers. First, we perform inverse modified error analysis of the ODE-nets using unrolled implicit schemes for ease of interpretation. It is shown that training an ODE-net using an unrolled implicit scheme returns a close approximation of an inverse modified differential equation (IMDE). In addition, we establish a theoretical basis for hyperparameter selection when training such ODE-nets, whereas current strategies usually treat numerical integration of ODE-nets as a black box. We thus formulate an adaptive algorithm which monitors the level of error and adapts the number of (unrolled) implicit solution iterations during the training process, so that the error of the unrolled approximation is less than the current learning loss. This helps accelerate training while maintaining accuracy. Several numerical experiments are performed to demonstrate the advantages of the proposed algorithm compared to nonadaptive unrollings and validate the theoretical analysis. We also note that this approach naturally allows for incorporating partially known physical terms in the equations, giving rise to what is termed "gray box" identification. [ABSTRACT FROM AUTHOR]

This paper presents the integration of a numerical structural model based on the redundancy matrix and experimental results of multi-layered randomized architected materials (MLRAM). It presents a combination of the relatively new field of architected materials with a load-independent performance indicator from theoretical structural mechanics. The redundancy matrix by itself provides a measure for structural assessment that is independent of a specific load case. Various layouts of the MLRAM samples and recorded testing allow the analysis of the redundancy distribution within the structure as it undergoes failure. An in-depth analysis of the tested MLRAM samples is provided, as they show a high degree of static indeterminacy and thus, multiple different load paths. A special focus lies on the change of the redundancy distribution as global progressive failure happens. Another focus is set on the investigation of the failure initiation, meaning that the redundancy distribution can help to identify critical elements. A simple introductory example shows the interdependence between the variation of the geometric location of nodes and the redundancy distribution. The study shows, that the distribution of static indeterminacy can be used as a measure to quantify vulnerability to failure and rank the individual element's importance. Furthermore, progressive collapse is identified as a series of local effects in the highly statically indeterminate MLRAM samples, underlining the fact that the spatial distribution of static indeterminacy is of central importance for the assessment of structural safety. [ABSTRACT FROM AUTHOR]

While humans can readily access the common magnitude of various codes such as digits, number words, or dot sets, it remains unclear whether this process occurs automatically, or only when explicitly attending to magnitude information. We addressed this question by examining the neural distance effect, a robust marker of magnitude processing, with a frequency-tagging approach. Electrophysiological responses were recorded while participants viewed rapid sequences of a base numerosity presented at 6 Hz (e.g., "2") in randomly mixed codes: digits, number words, canonical dot, and finger configurations. A deviant numerosity either close (e.g., "3") or distant (e.g., "8") from the base was inserted every five items. Participants were instructed to focus their attention either on the magnitude number feature (from a previous study), the parity number feature, a nonnumerical color feature or no specific feature. In the four attentional conditions, we found clear discrimination responses of the deviant numerosity despite its code variation. Critically, the distance effect (larger responses when base/deviant are distant than close) was present when participants were explicitly attending to magnitude and parity, but it faded with color and simple viewing instructions. Taken together, these results suggest automatic access to an abstract number representation but highlight the role of selective attention in processing the underlying magnitude information. This study therefore provides insights into how attention can modulate the neural activity supporting abstract magnitude processing. [ABSTRACT FROM AUTHOR]

Integral formulas represent a methodological basis for the determination of gravitational fields generated by planetary bodies. In particular, spherical integral transformations are preferred for their symmetrical properties with the integration domain being the entire surface of the sphere. However, global coverage of boundary values is rarely guaranteed. In practical calculations, we therefore split the spherical surface into a near zone and a far zone, for convenience, by a spherical cap. While the gravitational effect in the near zone can be evaluated by numerical integration over available boundary values, the contribution of the far zone has to be precisely quantified by other means. Far-zone effects for the isotropic integral transformations and those depending on the direct azimuth have adequately been discussed. On the other hand, this subject has only marginally been addressed for the spherical integral formulas that are, except for other variables, also functions of the backward azimuth. In this article, we significantly advance the existing geodetic methodology by deriving the far-zone effects for the two classes of spherical integral transformations: (1) the analytical solutions of the horizontal, horizontal–horizontal, and horizontal–horizontal–horizontal BVPs including their generalisations with arbitrary-order vertical derivative of respective boundary conditions and (2) spatial (vertical, horizontal, or mixed) derivatives of these generalised analytical solutions up to the third order. The integral and spectral forms of the far-zone effects are implemented in MATLAB software package, and their consistency is tested in closed-loop simulations. The presented methodology can be employed in upward/downward continuation of potential field observables or for a quantification of error propagation through spherical integral transformations. [ABSTRACT FROM AUTHOR]

Frequency Domain Thermoreflectance (FDTR) is a versatile technique used to measure the thermal properties of thin films, multilayer stacks, and interfaces that govern the performance and thermal management in semiconductor microelectronics. Reliable thermal property measurements at these length scales (≈10 nm to ≈10 μm), where the physics of thermal transport and phonon scattering at interfaces both grow in complexity, are increasingly relevant as electronic components continue to shrink. While FDTR is a promising technique, FDTR instruments are generally home-built; they can be difficult to construct, align, and maintain, especially for the novice. Our goal here is to provide a practical resource beyond theory that increases the accessibility, replicability, and widespread adoption of FDTR instrumentation. We provide a detailed account of unpublished insights and institutional knowledge that are critical for obtaining accurate and repeatable measurements of thermal properties using FDTR. We discuss component selection and placement, alignment procedures, data collection parameters, common challenges, and our efforts to increase measurement automation. In FDTR, the unknown thermal properties are fit by minimizing the error between the phase lag at each frequency and the multilayer diffusive thermal model solution. For data fitting and uncertainty analysis, we compare common numerical integration methods, and we compare multiple approaches for fitting and uncertainty analysis, including Monte Carlo simulation, to demonstrate their reliability and relative speed. The instrument is validated with substrates of known thermal properties over a wide range of isotropic thermal conductivities, including Borofloat silica, quartz, sapphire, and silicon. [ABSTRACT FROM AUTHOR]

We consider the problem of approximating the perimeter of an ellipse, for which there is no known finite formula, in the context of high-precision performance. Ellipses are broadly used in many fields, like astronomy, manufacturing, medical imaging, and geophysics. They are applied on large and nanoscales, and while numerical integration can be used to obtain precision measurements, having a finite formula can be used for modeling. We propose an iterative symbolic regression approach, utilizing the pioneering work of Ramanujan's second approximation introduced in 1914 and a known Padé approximation, leading to good results for both low and high eccentricities. Our proposed model is also compared with a very comprehensive historical collection of different approximations collated by Stanislav Sýkora. Compared with the best-known approximations in this centuries-old mathematical problem, our proposed model performs at both extremities while remaining consistent in mid-range eccentricities, whereas existing models excel only at one extremity. [ABSTRACT FROM AUTHOR]

This study aims to introduce a robust numerical approach to simulate complex small‐scale mediums such as trabecular bone tissue in form of a cylindrical specimen taken from human vertebra. Consideration of previous related studies indicates that there are several challenges in utilizing standard finite element (FE) techniques for the analysis of such biomechanical structures. This is mainly due to their time‐consuming procedure required for generating geometry conforming meshes. In this regard, the finite cell method (FCM) is an interesting alternative because it is based on the concept of the fictitious domain technique in which underlying meshes do not need to conform to the boundary of the domain. Since the considered trabecular bone tissue consists of a complex small‐scale internal morphology, generating a FE mesh is rather complicated. So, the application of the FCM can be justified by overcoming the mentioned shortcomings of FE methods for this problem. Using FCM, it is possible to simulate the mentioned trabecular cylinder from vertebral body using higher order cells of regular shapes where the geometry is taken care of through the numerical integration. The input for the present numerical tool corresponding to the complex internal morphology of the proposed tissue is given by a high‐resolution microCT scan. The outcome of the FCM will be compared to results obtained by mechanical testing of the specimen. [ABSTRACT FROM AUTHOR]

Hammer throwing is a motorically demanding sport in which the execution of the movement significantly influences the result, that is the throwing distance. There are many approaches for supporting technical training that are based on measurement technology and image capturing. The accelerations and locus curves of the athlete and hammer are recorded and compared. In this article, these methods are supplemented by a multi‐body simulation (MBS) of the hammer throw. The kinematics of the hand movement is described using a parameterized synthetic trajectory. Scalar parameters in the approach allow the trajectory to be modified. With a MBS model of the wire cable and the hammer, the movement of the hammer can be determined by numerical time integration from the hand's trajectory. As a result the final throwing distance after free flight phase can be analyzed. Due to the complex spatial motion of the hammer during the acceleration phase only heuristic methods can be used to optimize the maximum throwing distance. In a final step the optimized movement can be used to improve the athlete's training. [ABSTRACT FROM AUTHOR]

Damage is an undesirable and progressive process that ultimately leads to complete failure of materials. Obtaining a robust tool to precisely and reliably predict damage evolution behavior in ductile sheet metals is among the most crucial challenges for researchers and engineers. In this paper, first, based on the continuum damage mechanics (CDM) and the original Lemaitre's ductile damage model, a new 2D fast and straightforward version specialized for the plane stress conditions as well as a novel numerical integration algorithm are fully presented. Additionally, a modified numerical approach, founded on the bisection method is suggested for determining the material-dependent ductile damage parameter of the model. Then, an explicit subroutine is developed and implemented to numerically predict damage evolution behavior in different ductile sheet metals and shapes. Finally, the numerical simulation results of damage initiation, growth, and crack onset are attained and validated. The numerical simulation predicted results reveal that the novel offered version of the Lemaitre's ductile damage model in conjunction with the enhanced numerical approach is able to more rapidly predict the material-dependent ductile damage parameter and also the evolution of damage in ductile sheet metals under various loading and boundary conditions. [ABSTRACT FROM AUTHOR]

We consider the effect of a shear flow which has, without loss of generality, a zero mean flow rate, on a Kolmogorov–Petrovskii–Piscounov (KPP)‐type model in the presence of a discontinuous cutoff at concentration u=uc$u = u_c$. In the long‐time limit, a permanent‐form traveling wave solution is established which, for fixed uc>0$u_c>0$, is unique. Its structure and speed of propagation depends on A$A$ (the strength of the flow relative to the propagation speed in the absence of advection) and B$B$ (the square of the front thickness relative to the channel width). We use matched asymptotic expansions to approximate the propagation speed in the three natural cases A→∞$A\rightarrow \infty$, A→0$A\rightarrow 0$, and A=O(1)$A=O(1)$, with particular associated orderings on B$B$, while uc∈(0,1)$u_c\in (0,1)$ remains fixed. In all the cases that we consider, the shear flow enhances the speed of propagation in a manner that is similar to the case without cutoff (uc=0$u_c=0$). We illustrate the theory by evaluating expressions (either directly or through numerical integration) for the particular cases of the plane Couette and Poiseuille flows. [ABSTRACT FROM AUTHOR]

Gridpoint discretization of the model has a significant impact on the accuracy of finite-difference seismic waveform simulations. Discretizing the discontinuous velocity model using local point medium parameters can lead to artefact diffraction caused by the stair-step representation and inaccuracies in calculated waveforms due to interface errors, particularly evident when employing coarse grids. To accurately represent model interfaces and reduce interface errors in finite-difference calculations, various equivalent medium parametrization methods have been developed in recent years. Most of these methods require volume-integrated averaging calculations of the medium parameter values within grid cells. The simplest way to achieve this volume averaging is to apply numerical integration averaging to all grid cells. However, this approach demands considerable computational time. To address this computational challenge, we propose employing a set of auxiliary grids to identify which grid cells intersected by the welded interface and perform volume averaging only on these specific cells, thereby reducing unnecessary computational overhead. Additionally, we present a 3-D tilted transversely isotropic equivalent medium parametrization method, which effectively suppresses interface errors and artefact diffraction under the application of coarse grids. We also provide an approach for computing the normal direction of the interface, which is essential for the tilted transversely isotropic equivalent medium parametrization. Numerical tests validate the accuracy of the tilted transversely isotropic equivalent medium parametrization method and demonstrate the practicality of the implementation proposed in this paper for complex models. [ABSTRACT FROM AUTHOR]

Density power divergence (DPD) is designed to robustly estimate the underlying distribution of observations, in the presence of outliers. However, DPD involves an integral of the power of the parametric density models to be estimated; the explicit form of the integral term can be derived only for specific densities, such as normal and exponential densities. While we may perform a numerical integration for each iteration of the optimization algorithms, the computational complexity has hindered the practical application of DPD-based estimation to more general parametric densities. To address the issue, this study introduces a stochastic approach to minimize DPD for general parametric density models. The proposed approach can also be employed to minimize other density power-based γ -divergences, by leveraging unnormalized models. We provide R package for implementation of the proposed approach in https://github.com/oknakfm/sgdpd. [ABSTRACT FROM AUTHOR]

In this paper, a numerical strategy is introduced for solving a class of linear fractional-order Darboux problem that includes the Caputo derivative. The presented strategy is grounded on the Newton-Cotes quadrature rule and is established by implementing Lagrange interpolation polynomial. A formula is developed to evaluate the two-dimensional fractional integrals by using the multiplicative integration strategy. Then, this formula is employed to derive a scheme for solving a class of fractional-order Darboux problem. The accuracy and efficiency of all the presented schemes are illustrated through numerical experiments. Furthermore, the estimation of the upper bounds of error in the numerical approximation for the proposed multiplicative integration strategy is established. [ABSTRACT FROM AUTHOR]

New families of composition methods with processing of order 4 and 6 are presented and analyzed. They are specifically designed to be used for the numerical integration of differential equations whose vector field is separated into three or more parts which are explicitly solvable. The new schemes are shown to be more efficient than previous state-of-the-art splitting methods. [ABSTRACT FROM AUTHOR]

Uncertainty of a geoscientific map derived from data sampled by sensory engagement of human experts cannot be quantified from within the processing chain followed to produce the map due to subjective components in the underlying data. Nevertheless, quantified uncertainty associated with such maps would be essentially required for correct information retrieval from such maps. An approach mimicking an expert elicitation through digital agents in an information fusion procedure is suggested to quantify the trustworthiness of a partially subjective map (such as a soil map or any other geoscientific map inherently linked to partial subjectivity, e.g., a geological map). This procedure links a partially subjective map with collocated maps resulting from technical measurements provided with quantified uncertainty. Variation of methodology in this approach results in an ensemble of maps with variable degree of matching with the partially subjective map which allows for probabilistic statements about the trustworthiness of the partially subjective map. This enables including partially subjective maps in further data integration relying on numerical analysis, e.g., in the context of computational modeling or machine learning. By being able to assign a quantitative trustworthiness to a partially subjective map the risk of over-utilization of this map is reduced. [ABSTRACT FROM AUTHOR]

Panel count regression is often required in recurrent event studies, where the interest is to model the event rate. Existing rate models are unable to handle time-varying covariate effects due to theoretical and computational difficulties. Mean models provide a viable alternative but are subject to the constraints of the monotonicity assumption, which tends to be violated when covariates fluctuate over time. In this paper, we present a new semiparametric rate model for panel count data along with related theoretical results. For model fitting, we present an efficient EM algorithm with three different methods for variance estimation. The algorithm allows us to sidestep the challenges of numerical integration and difficulties with the iterative convex minorant algorithm. We showed that the estimators are consistent and asymptotically normally distributed. Simulation studies confirmed an excellent finite sample performance. To illustrate, we analyzed data from a real clinical study of behavioral risk factors for sexually transmitted infections. [ABSTRACT FROM AUTHOR]

A new solution for the analysis of slitted parallel‐plate waveguide is proposed using the method of Kobayashi Potential (KP). The interior and exterior problems are studied for the TE and TM polarizations. Simplified forms of Weber‐Schafheitlin (WS) integrals are utilized for problem formulation. The Fourier function space is exploited to construct the governing linear system of equations. A simple strategy is suggested for the evaluation of the required integrals. Numerical results are validated through convergence analysis and available reports based on the Moment Method (MM). It is shown that the KP is superior to the conventional MM in the sense of tracking edge singularities, especially when the radiation problem is of interest. Key Points: A new solution for the analysis of slitted parallel‐plate waveguides is proposed using the method of Kobayashi PotentialA direct numerical integration method is proposed to efficiently evaluate semi‐infinite integralsSupersedes the conventional moment method for the problem at hand due to precise tracking of edge singularities [ABSTRACT FROM AUTHOR]

Kang Feng proposed the symplectic geometric algorithms for Hamiltonian systems at Beijing "International Symposium on Differential Geometry and Differential Equations" in August 1984, opening up a new field of research. Over the past 40 years, geometric numerical integration for dynamical systems has been irreplaceably applied in numerous fields, including celestial mechanics, plasma physics, fluid mechanics, biochemistry, meteorological forecasting, seismic exploration, data science and artificial intelligence. This paper mainly summarizes the achievements of geometric numerical integration for dynamical systems in China over the past 40 years. [ABSTRACT FROM AUTHOR]

In this paper, we present a fitted numerical scheme for singularly perturbed delay differential equations with integral boundary conditions. To develop the scheme, the exact and approximate rules of integration with finite difference approximations of the first derivative are used. In the developed scheme, a fitting factor is introduced whose value is evaluated from the theory of singular perturbation. The Runge-Kutta method of order four is used to solve the reduced problem, and for the integral boundary condition, Composite Simpson's rule of integration is applied. The proposed method is shown to be second-order convergent. Numerical illustrations for various values of perturbation parameters are presented to validate the proposed method. The numerical results clearly show the high accuracy and order of convergence of the proposed scheme as compared to some of the results available in the literature. [ABSTRACT FROM AUTHOR]

This paper proposes a nonlinear Model Predictive Control (MPC) method based on Physics-Informed Neural Networks (PINNs), aimed at enhancing the trajectory tracking performance of Automated Guided Vehicles (AGVs) in complex dynamic environments. Traditional physical models often face the challenges of computational inefficiency and insufficient control precision when dealing with complex dynamic systems. However, by integrating physical laws directly into the training process of neural networks, PINNs can effectively learn and capture the kinematic characteristics of vehicles, replacing traditional nonlinear ordinary differential equation models and thus significantly enhancing computational efficiency and control performance. During the model-training phase, this study further incorporates the Theory of Functional Connections (TFC) and adaptive loss balancing strategies to efficiently solve ODE problems without relying on numerical integration and optimize the control strategy. This combined approach not only reduces computational complexity, but also improves the robustness and precision of the control strategy in varying environments. Numerical simulations demonstrate that this method offers significant advantages in AGV trajectory-tracking tasks, manifested in higher computational efficiency and precise control performance. The proposal of the PINN-MPC method provides new theoretical support and innovative methods for real-time complex system control, with important research and application potential, and is expected to play a key role in future intelligent control systems. [ABSTRACT FROM AUTHOR]

This paper presents a dynamic homotopy technique that can be used to calculate a preliminary result for a power flow problem (PFP). This result can then be used as an initial estimate to efficiently solve the PFP using either the classical Newton-Raphson (NR) method or its fast decoupled version (FDXB) while still maintaining high accuracy. The preliminary stage for the dynamic homotopy problem is formulated and solved by employing integration techniques, where implicit and explicit schemes are studied. The dynamic problem assumes an initial condition that coincides with the initial estimate for a traditional iterative method such as NR. In this sense, the initial guess for the FPF is adequately set as a flat start, which is a starting for the case when this initialization is of difficult assignment for convergence. The static homotopy method requires a complete solution of a PFP per homotopy pathway point, while the dynamic homotopy is based on numerical integration methods. This approach can require only one LU factorization at each point of the pathway. Allocating these points properly helps avoid several PFP resolutions to build the pathway. The hybrid technique was evaluated for large-scale systems with poor conditioning, such as a 109,272-bus model and other test systems under stressed conditions. A scheme based on the implicit backward Euler scheme demonstrated the best performance among other numerical solvers studied. It provided reliable partial results for the dynamic homotopy problem, which proved to be suitable for achieving fast and highly accurate solutions using both the NR and FDXB solvers. [ABSTRACT FROM AUTHOR]

The main goal of this paper is to develop a new class of sixth- and fourth-order implicit Runge–Kutta methods to treat linear and nonlinear initial value ordinary differential equations (ODEs) in applied science and engineering. In this regard, a completely unconventional approach is taken to derive the new formulations. They are derived through a computational approach without involving in the rigorous theory of order conditions. The new formulation has two distinctive parts, namely integration and interpolation. In the first part, we introduce a form of multi-stage single-step numerical integrator with unknown weights. These weights are determined by four simple interconnectivity rules that relate them to minimize the error of the integrator. Some of these rules are based on our expertise gathered from the available prominent quadratures. However, the most important one, the so-called fundamental weighting rule (FWR), is obtained from evolutionary and statistical computations. The second part of this research focuses on developing efficient tools for evaluating the internal stages of the integrator. Accordingly, a series of strong Hermite interpolators has been extended to approximate the solution values at the internal stages. They effectively collaborate with the integrator in several numerical algorithms, the so-called α I I - (q + r) P algorithms, to solve applied ODEs. Development of the integrator, its weighting rules, and the interpolators constitutes the central contribution of this research. Numerical studies demonstrate that the presented algorithms exhibit a high level of accuracy when approximating high-frequency problems as well as long-term solutions of linear and nonlinear ODEs. [ABSTRACT FROM AUTHOR]

It is well known that the roughness of a wall plays a crucial role in determining the passive earth pressure that is exerted on a rigid wall. While the effects of positive wall roughness have been extensively studied in the past few decades, the study of passive earth pressure with negative wall friction is rarely found in the literature. This study aims to provide a precise solution for negative friction walls under passive wall conditions. The research is initiated by adopting a radial stress field for the cohesionless backfill and employs the concept of stress self-similarity. The problem is then formulated in a way that a statically admissible stress field be developed throughout an analyzed domain using a two-step numerical framework. The framework involves the successful execution of numerical integration, which leads to the exploration of the statically admissible stress field in cohesionless backfills under negative wall friction. This, in turn, helps to shed light on the mechanism of load transfer in such situations so that reliable design charts and tables be provided for practical uses. The study continues with a soft computing model that leads to more robust and effective designs for earth-retaining structures under various negative wall frictions and sloping backfills. [ABSTRACT FROM AUTHOR]

To solve the problem of controlling mining in the open-pit mine end slope fire-burned area, applying multivariate function fitting to the roof and floor modeling of multi-coal seam open pit mines, introducing the factor of coal quality changes in the fire-burned area, determining coal quality information at each location through proximate analysis of coal, to establish the net profit model of the mining area, it is determined the net profit of each mining position by numerical integration, the final mining position was determined without failure by calculating the slope stability based on the numerical simulation of strength reduction. Taking the Dananhu No. 2 open-pit mine in Hami, Xinjiang, China as the engineering background, the fire-burned area III within the southern end slope boundary of the first mining area is 240 m. It was finally determined that the optimal mining position is when the advancement degree is 182 m, the ultimate pit slope angle is 25°, the three-dimensional slope stability is 1.305, the profit is 671.96 million yuan, The deep boundary of the southern end slope fire-burned area of the slope is reduced by 58 m. This paper solves the problem of end slope mining in Dananhu No. 2 mine, and maximizes its net profit under the condition of ensuring safe production. [ABSTRACT FROM AUTHOR]

Roll coating is a popular method for applying a thin coating film to a continuous substrate, such as paper or foil. This study aims to investigate analytically the fluid flow through counter rotating rolls using a non-Newtonian model. The governing equation for the constitutive of the Oldroyd-B as a non-Newtonian fluid with momentum equation has been discovered. The nondimensionalizing of the fluid flow equations is done by using suitable dimensionless parameters. The equations are then simplified by using Lubrication Approximation Theory (LAT) to obtain the solution for various quantities. Analytical solutions for the velocity distribution, pressure and pressure gradients have been obtained by regular perturbation method. Numerical integration has been used to calculate separation point, coating thickness, separation force and power input of the fluid. The effect of involved parameter such as Weissenberg number We and viscosity on velocities, pressure gradient and pressure is presented in a variety of graphs and several other results are shown in tables. It has been observed that as the modified capillary number N C a 2 increases, the separation point moves toward the nip region, whereas the coating thickness declines. It has been witnessed that the We serves as the controlling parameter for flow rate, pressure distribution and power input, whereas for the coating thickness, the separation force increases, which are important for coating industries. [ABSTRACT FROM AUTHOR]

For survival analysis applications we propose a novel procedure for identifying subgroups with large treatment effects, with focus on subgroups where treatment is potentially detrimental. The approach, termed forest search, is relatively simple and flexible. All‐possible subgroups are screened and selected based on hazard ratio thresholds indicative of harm with assessment according to the standard Cox model. By reversing the role of treatment one can seek to identify substantial benefit. We apply a splitting consistency criteria to identify a subgroup considered "maximally consistent with harm." The type‐1 error and power for subgroup identification can be quickly approximated by numerical integration. To aid inference we describe a bootstrap bias‐corrected Cox model estimator with variance estimated by a Jacknife approximation. We provide a detailed evaluation of operating characteristics in simulations and compare to virtual twins and generalized random forests where we find the proposal to have favorable performance. In particular, in our simulation setting, we find the proposed approach favorably controls the type‐1 error for falsely identifying heterogeneity with higher power and classification accuracy for substantial heterogeneous effects. Two real data applications are provided for publicly available datasets from a clinical trial in oncology, and HIV. [ABSTRACT FROM AUTHOR]